Take pi (3.14159...) and raise it to the fourth power; then add that to the value of pi raised to the fifth power. The total (403.428...) is exceedingly close to e (2.71828...) raised to the sixth power. Coincidence? Sure, in the sense that two things have "coincided", i.e., come together. But what kind of coincidence is this?

About 15 years ago a friend (JB) and I tried to come up with a taxonomy of coincidences --- or at least some useful categories to describe such things. We never finished or properly wrote it up ... but as an interim snapshot, here are some examples of our system:

Mere coincidence --- a purely accidental alignment of objects, like some of the constellations of stars in the sky

Definitional coincidence --- a match that comes because something was arbitrarily set that way, like the precise ratio (2.54) between centimeters and inches

Suggestive coincidence --- a relationship that points to something more significant, like the jigsaw-puzzle fit between Africa and South America

Causal coincidence --- a pattern that emerges because one part influences, triggers, or leads to another

Of course, what's "deep" to one observer may be transparently obvious to another. Over time, a coincidence may shift from one class to another, as people understand it better. And some coincidences may belong in multiple bins, depending on how they're viewed or analyzed.

-----Hmmm. Coincidence may be that we don't yet understand the correlation. I am suspicious of a greater piece of unknown information whenever I hear the word coincidence. Take the randomness of galaxies, stars. I see solar systems as big atoms and infinity as more about size than time. Judy Decker

Many years ago I read The Roots of Coinsidence by Aldous Huxley. It gave me pause to think about what we call the "real" or physical world and what it's made of. Then I stubbed my toe and came back to my senses.